Question: Simplify the following expression: $\dfrac{5n^4}{2n^4}$ You can assume $n \neq 0$.
Answer: $ \dfrac{5n^4}{2n^4} = \dfrac{5}{2} \cdot \dfrac{n^4}{n^4} $ To simplify $\frac{5}{2}$ , find the greatest common factor (GCD) of $5$ and $2$ $5 = 5$ $2 = 2$ $ \mbox{GCD}(5, 2) = = 1 $ $ \dfrac{5}{2} \cdot \dfrac{n^4}{n^4} = \dfrac{1 \cdot 5}{1 \cdot 2} \cdot \dfrac{n^4}{n^4} $ $\phantom{ \dfrac{5}{2} \cdot \dfrac{4}{4}} = \dfrac{5}{2} \cdot \dfrac{n^4}{n^4} $ $ \dfrac{n^4}{n^4} = \dfrac{n \cdot n \cdot n \cdot n}{n \cdot n \cdot n \cdot n} = 1 $ $ \dfrac{5}{2} \cdot 1 = \dfrac{5}{2} $